As the event selection was exactly the same as in the previous analyses, we reused the results of the background estimation from them.
The main background in the NA64 "visible mode" configuration comes from the electroproduction of \(K^0_S\)  and their decays
\(K^0_S \rightarrow \pi ^0 \pi ^0\)  in flight, followed by conversion of one of the decay photons. After optimization of the setup in 2018 this
background, determined from data, amounted to less than 0.005 events per \(10^{10}\)  EOT [1]}. The main background
in the "invisible mode" configuration comes from neutral hadron production by electrons in the target. These neutral hadrons either pass without
interaction the first HCAL module and deposit energy in the downstream modules HCAL2,3, or completely escape detection because of insufficient
aperture of the HCAL. These backgrounds, of the order of 0.1 events, were also determined from data [2]}, [3]}.
